Let S be the set of odd positive integers. A function F : N → S is defined by F (n) = k, where k is that odd positive integer for which 3n + 1 = (2^m)k for some nonnegative integer m. (That is, k is what's left after factoring as many 2's as possible out of 3n + 1.) Determine whether F is one-to-one, and/or onto.